Girdling roots are as bad for a plant as girdled stems. You know the girdled stem - someone forgets to loosen or untie that rope around the limb and the rope becomes part of the bark. It's a death sentence for the limb and likely to decrease the trees' resistance to diseases and pests. The same for roots!
You can often see girdled roots at the soil surface (though they can, and often do, occur well below the soil surface). They are roots that are turning and circling around the trunk often impeding other roots.
They result from the clay and rock filled soils we live with here in East TN, as well as poor management practices in nurseries, and poor planning in the landscape.
You can address the surface roots your self if you are sufficiently brave (or is cavalier a better word;?....) The ones below the surface you will need a specialist (an arborist), like me, to excavate the root zone using an air-spade. It's not cheap but it will keep the life of your tree a longer healthier one and help every other plant in the vicinity of soil-aeration.
Using a very sharp blade (hand saw) for diameters <10 inches, make a clean cut through the girdling root. For roots dieters 10 - 15" cut a "pie" wedge from the root. You'll hear the root 'give' as you near the end of your cut. The cut doesn't need to penetrate the full root with this cut but 3/4 of the root. Any root >15" diameter DONT cut. Call me or an arborist instead to explore other options. Clear as mud (pardon the pun)? If yes, contact me!
(last picture is from Purdue University's website)